Continuous rod is now replacing sucker rod strings consisting of multiple connected sucker rods lengths in oil well pumping applications. A continuous rod only requires two connections: one at the top and one at the bottom. Reducing the number of connections serves to reduce the severity of both tubing and rod wear. When continuous rod is used, there is no need for centralizers and rods guides in most wells. However, it has been discovered that excessive wear is occurring in some wells. Upon investigation it has been determined that the wells in question have one or more curved sections. Some such wells have what could be termed a serpentine profile. Although centralizers per se are well known, there are presently not any centralizers that are particularly adapted for use on continuous rod. What is required is a centralizer suited for use with continuous rod.